Characterizing Robust Solution Sets of Convex Programs under Data Uncertainty

V. Jeyakumar (), G. M. Lee () and G. Li ()
Additional contact information
V. Jeyakumar: University of New South Wales
G. M. Lee: Pukyong National University
G. Li: University of New South Wales

Journal of Optimization Theory and Applications, 2015, vol. 164, issue 2, No 2, 407-435

Abstract: Abstract This paper deals with convex optimization problems in the face of data uncertainty within the framework of robust optimization. It provides various properties and characterizations of the set of all robust optimal solutions of the problems. In particular, it provides generalizations of the constant subdifferential property as well as the constant Lagrangian property for solution sets of convex programming to robust solution sets of uncertain convex programs. The paper shows also that the robust solution sets of uncertain convex quadratic programs and sum-of-squares convex polynomial programs under some commonly used uncertainty sets of robust optimization can be expressed as conic representable sets. As applications, it derives robust optimal solution set characterizations for uncertain fractional programs. The paper presents several numerical examples illustrating the results.

Keywords: Convex optimization problems with data uncertainty; Robust optimization; Optimal solution set; Uncertain convex quadratic programs; Uncertain sum-of-squares convex polynomial programs; 90C25; 90C20; 90C46 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (12)

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DOI: 10.1007/s10957-014-0564-0

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